The Principle of Diminishing Chip Value

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Understanding the real value of chips is one of the most important skills in SNGs and a key to understand crucial concepts like the Independent Chip Model. In this video you will learn why chips in SNGs have different value than in cash games and why you should distinguish between chip expected value and monetary expected value.

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In this video you will learn Why chips in SNGs have different value than in cash games, how to understand the real value of chips in SNGs And why y..

The principle of diminishing chip value

In this video you will learn Why chips in SNGs have different value than in cash games, how to understand the real value of chips in SNGs And why you should distinguish between chip expected value and monetary expected value

To understand the real value of your stack, you need to see the relationship between the quantity of your chips and their real value. In the following example you buy-in to a cash game for $10 and get $10 in chips. Now take a look at the following hand. Seven players fold and a maniac who sits in the SB raises all-in. You make an easy call with your aces and win the hand. Assuming that there is no rake, you have doubled your stack.

At the beginning your stack was worth $10 If you stand up from the table now, you have $20, which means that by doubling your stack you have also doubled your money. As you can see, in cash games the number of chips is equal to their value.

Have a look at this example from a $10 9-man SNG. For simplicity’s sake, suppose it’s rake-free. Each player buys-in for $10 and gets the same stack. Now suppose you have finished in 1st place, and thereby won all the chips. You have now multiplied your stack by nine.

But, if you take a look at the payout structure, you see that the prize for first place is $45. As you remember, when you started the SNG your stack was worth $10. However, after you’ve multiplied it by nine, you didn’t get $90, but only $45, which represents 50% of the prize pool. (pause) What follows from this observation is that the chips you’ve won are worth less than the ones you’ve risked to win them. This shows that in SNGs the number of chips and their value are not directly correlated.

From this observation the principle of diminishing chip value can be derived: a chip you are about to win in a SNG is not necessarily worth as much as the one you're risking to win it. Since chips won in SNGs are not necessarily worth as much as ones you already have, it can be said that you risk more “value” in order to win less “value”. That is why in SNGs you need more equity than in cash games in order to call a bet profitably.

In respect to the above, we express the difference between a given number of chips and their value by using two types of expected value: chip expected value and monetary expected value. Chip expected value is the average number of chips you can expect as the result of an action. Monetary expected value is the average amount of money you can expect as the result of an action, based on your current prize pool equity. $EV is the monetary equivalent of cEV. $EV is also used to describe the monetary value of a given stack.

To fully understand different kinds of expected value, consider the following example from a 10-seater Double Or Nothing SNG. It's a type of a SNG which awards 5 of 10 players double their $10 buy-in as a prize. In order to simplify calculations, once again suppose there is no rake. The first hand of the game has just been dealt. Since the blinds are very small, it can be assumed that all players have equal stacks worth $10 each. Five players have gone all-in and two others have folded. You sit on the button and assume that with pocket aces your equity in this spot is 40%. You also assume that if you call, both SB and BB will fold. Let’s take a look at the chip expected value of your potential call. To calculate it, you multiply the total pot size by your equity and then deduct the chips you put at risk . You see that by calling you win 2,112 chips on average. Therefore this call is very profitable in terms of chips. To calculate the monetary value of your potential call You multiply your potential prize by your equity. Instead of deducting chips you put at risk you deduct their current monetary value which is – as explained before - $10. Therefore, in terms of money, you lose $2 on average - calling is here unprofitable. As you can see, in this situation calling earns chips, but loses money. Since a given decision can be profitable in terms of chips but not profitable in terms of money, you should always think about your moves in terms of their real, monetary profitability instead of profitability measured in chips. That’s exactly why distinguishing between chip expected value and monetary expected value is such a crucial ability in SNGs.

In this lesson you have learned how you should think about and recognise the value of your chips. To fully master the material, take a look at the most important conclusions: The principle of diminishing value means that a chip you are about to win in a SNG is not necessarily worth as much as the one you're risking to win it. In SNGs you need more equity than in cash games in order to call a bet profitably. Chip expected value is the average number of chips you can expect as the result of an action. Monetary expected value is the average amount of money you can expect as the result of an action, based on your current prize pool equity. A given decision can be profitable in terms of chips but not profitable in terms of money.

Isn´t it true, that our $EV in the last example is even lower than -2$?
The EV of the call is clear, but our opportunity of calling is folding and the worth of our stack after a fold is higher than 10$. Before this situation it was worth 10$ but after this hand we are most likely up against just 6 or 7 opponents so that we are much closer to the money. with 6 Players left and 5 of these player have a stack of 1500 chips (inluding us) or stack should have have a worth of 15%-17$.

Entire example's goal is to show that a given decision may earn chips, but lose money. In our example the decision we consider is a call. I agree that calculating monetary value of a fold is interesting and that it proves even more how wrong the potential call is, but that's not the point here. We don't need to show it here. I'd say even more - we don't want to show it here, as:
- it's not necessary to explain what we're trying to show,
- it might be too difficult and confusing,
- it's basically impossible without explaining entire idea of the ICM.

It doesn't make our calculation wrong, as we don't take folding into account at all, we just want to show one simple thing - calling earns chips but loses money.

When it comes to the value of the stack we put at risk ($10) - it's all about having some reference point. For the sake of simplicity we've decided to show it in reference to the value of our stack before the hand is dealt. Of course, ideally we should take into account the fact that several players have gone all-in before us (so basically in reference to the value of our stack in the next hand), but again – it would make entire process super complicated and wouldn’t be possible without explaining the fundamentals of the ICM.